相关论文: A stochastic gradient descent approach with partit…

Optimization problems with continuous data appear in, e.g., robust machine learning, functional data analysis, and variational inference. Here, the target function is given as an integral over a family of (continuously) indexed target…

We consider chance-constrained problems with discrete random distribution. We aim for problems with a large number of scenarios. We propose a novel method based on the stochastic gradient descent method which performs updates of the…

Solving large tensor linear systems poses significant challenges due to the high volume of data stored, and it only becomes more challenging when some of the data is missing. Recently, Ma et al. showed that this problem can be tackled using…

We propose a novel stochastic gradient descent method for solving linear least squares problems with partially observed data. Our method uses submatrices indexed by a randomly selected pair of row and column index sets to update the iterate…

Stochastic gradient descent (SGD) is a promising method for solving large-scale inverse problems, due to its excellent scalability with respect to data size. In this work, we analyze a new data-driven regularized stochastic gradient descent…

In this work we investigate the practicality of stochastic gradient descent and recently introduced variants with variance-reduction techniques in imaging inverse problems. Such algorithms have been shown in the machine learning literature…

In this work, we investigate a stochastic gradient descent method for solving inverse problems that can be written as systems of linear or nonlinear ill-posed equations in Banach spaces. The method uses only a randomly selected equation at…

The large-scale focusing inversion of gravity and magnetic potential field data using $L_1$-norm regularization is considered. The use of the randomized singular value decomposition methodology facilitates tackling the computational…

This paper introduces two variational inference approaches for infinite-dimensional inverse problems, developed through gradient descent with a constant learning rate. The proposed methods enable efficient approximate sampling from the…

The paper looks at a scaled variant of the stochastic gradient descent algorithm for the matrix completion problem. Specifically, we propose a novel matrix-scaling of the partial derivatives that acts as an efficient preconditioning for the…

Decentralized methods to solve finite-sum minimization problems are important in many signal processing and machine learning tasks where the data is distributed over a network of nodes and raw data sharing is not permitted due to privacy…

Stochastic gradient algorithms are the main focus of large-scale optimization problems and led to important successes in the recent advancement of the deep learning algorithms. The convergence of SGD depends on the careful choice of…

Stochastic gradient algorithms have been the main focus of large-scale learning problems and they led to important successes in machine learning. The convergence of SGD depends on the careful choice of learning rate and the amount of the…

We focus on solving constrained convex optimization problems using mini-batch stochastic gradient descent. Dynamic sample size rules are presented which ensure a descent direction with high probability. Empirical results from two…

Stochastic gradient descent (SGD) method is popular for solving non-convex optimization problems in machine learning. This work investigates SGD from a viewpoint of graduated optimization, which is a widely applied approach for non-convex…

It seems that in the current age, computers, computation, and data have an increasingly important role to play in scientific research and discovery. This is reflected in part by the rise of machine learning and artificial intelligence,…

We study the problem of estimating low-rank matrices from linear measurements (a.k.a., matrix sensing) through nonconvex optimization. We propose an efficient stochastic variance reduced gradient descent algorithm to solve a nonconvex…

We consider the problem of denoising with the help of prior information taken from a database of clean signals or images. Denoising with variational methods is very efficient if a regularizer well adapted to the nature of the data is…

We develop a distributed stochastic gradient descent algorithm for solving non-convex optimization problems under the assumption that the local objective functions are twice continuously differentiable with Lipschitz continuous gradients…

Seismic datasets contain valuable information that originate from areas of interest in the subsurface; such seismic reflections are however inevitably contaminated by other events created by waves reverberating in the overburden.…